Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×Q8×C157 ⋊ C4 |
| Sylow | C157 ⋊ #419 |
150 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,157|a^2=e,b^2=f,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^129,c^b=cf,d^b=df,g^e=g^156412 conjugacy classes — view the full character table.
| maximal subgroup of | #34115988, #34115989, #34116135, … |
| maximal normal subgroup of | #34115988, #34115989, #34116135, … |
| maximal quotient of | #34115438, #34115439, #34115440, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1542);